{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2-D Gaussian Distribution and HMC, SGHMC, SGLD, ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "from jax import config\n",
    "import jax\n",
    "from jax import numpy as jnp\n",
    "import numpy as onp\n",
    "import time\n",
    "import tqdm\n",
    "import optax\n",
    "import functools\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from bnn_hmc.utils import losses\n",
    "from bnn_hmc.utils import train_utils\n",
    "from bnn_hmc.utils import tree_utils\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = jnp.zeros([2,])\n",
    "# sigma = jnp.array([[1., .5], [.5, 1.]])\n",
    "sigma = jnp.array([[1.e-4, 0], [0., 1.]])\n",
    "sigma_l = jnp.linalg.cholesky(sigma)\n",
    "sigma_inv = jnp.linalg.inv(sigma)\n",
    "sigma_det = jnp.linalg.det(sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = onp.random.multivariate_normal(onp.asarray(mu), onp.asarray(sigma), size=1000)\n",
    "plt.scatter(samples[:, 0], samples[:, 1], alpha=0.3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "# def fake_model_forward(params, _, _, _, _):\n",
    "#     return params, None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_density_fn(params):\n",
    "    assert params.shape == mu.shape, \"Shape error\"\n",
    "    diff = params - mu\n",
    "    \n",
    "    k = mu.size\n",
    "    \n",
    "    log_density = -jnp.log(2 * jnp.pi) * k / 2\n",
    "    log_density -= jnp.log(sigma_det) / 2\n",
    "    log_density -= diff.T @ sigma_inv @ diff / 2\n",
    "    return log_density\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_likelihood_fn(_, params, *args, **kwargs):\n",
    "    return log_density_fn(params), jnp.array(jnp.nan)\n",
    "\n",
    "def log_prior_fn(_):\n",
    "    return 0.\n",
    "\n",
    "def log_prior_diff_fn(*args):\n",
    "    return 0.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "fake_net_apply = None\n",
    "fake_data = jnp.array([[jnp.nan,],]), jnp.array([[jnp.nan,],])\n",
    "fake_net_state = jnp.array([jnp.nan,])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## HMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Leapfrog steps per iteration: 16\n"
     ]
    }
   ],
   "source": [
    "step_size = 1e-1\n",
    "trajectory_len = jnp.pi / 2\n",
    "max_num_leapfrog_steps = int(trajectory_len // step_size + 1)\n",
    "print(\"Leapfrog steps per iteration:\", max_num_leapfrog_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "update, get_log_prob_and_grad = train_utils.make_hmc_update(\n",
    "    fake_net_apply, log_likelihood_fn, log_prior_fn, log_prior_diff_fn,\n",
    "    max_num_leapfrog_steps, 1., 0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial log-prob and grad values\n",
    "# params = jnp.ones_like(mu)[None, :]\n",
    "params = jnp.ones_like(mu)\n",
    "log_prob, state_grad, log_likelihood, net_state = (\n",
    "    get_log_prob_and_grad(fake_data, params, fake_net_state))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(DeviceArray(-2.3607028, dtype=float32),\n",
       " DeviceArray([-0.6666667, -0.6666667], dtype=float32),\n",
       " DeviceArray(-2.3607028, dtype=float32),\n",
       " ShardedDeviceArray([nan], dtype=float32))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_prob, state_grad, log_likelihood, net_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [03:28<00:00,  2.40it/s]\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 500\n",
    "all_samples = []\n",
    "key = jax.random.PRNGKey(0)\n",
    "\n",
    "for iteration in tqdm.tqdm(range(num_iterations)):\n",
    "\n",
    "    (params, net_state, log_likelihood, state_grad, step_size, key,\n",
    "     accept_prob, accepted) = (\n",
    "        update(fake_data, params, net_state, log_likelihood, state_grad,\n",
    "               key, step_size, trajectory_len, True))\n",
    "    \n",
    "    if accepted:\n",
    "        all_samples.append(onp.asarray(params).copy())\n",
    "\n",
    "#     print(\"It: {} \\t Accept P: {} \\t Accepted {} \\t Log-likelihood: {}\".format(\n",
    "#             iteration, accept_prob, accepted, log_likelihood))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_samples_cat = onp.stack(all_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(all_samples_cat[:, 0], all_samples_cat[:, 1], alpha=0.3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SGHMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bnn_hmc.core import sgmcmc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lr = 1.e-2\n",
    "lr = 1.e-4\n",
    "mom = 0.95\n",
    "lr_schedule = train_utils.make_cosine_lr_schedule_with_burnin(lr, lr, 1)\n",
    "optimizer = sgmcmc.sgld_gradient_update(lr_schedule, momentum_decay=mom, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = jnp.ones_like(mu)\n",
    "opt_state = optimizer.init(params)\n",
    "fake_net_state = jnp.array([jnp.nan,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgmcmc_train_epoch = train_utils.make_sgd_train_epoch(\n",
    "    fake_net_apply, log_likelihood_fn, log_prior_fn, optimizer, num_batches=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:10<00:00, 942.44it/s]\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 10000\n",
    "num_devices = 1\n",
    "all_samples = []\n",
    "key = jax.random.PRNGKey(0)\n",
    "key = jax.random.split(key, num_devices)\n",
    "save_freq = 10\n",
    "\n",
    "for iteration in tqdm.tqdm(range(num_iterations)):\n",
    "    params, _, opt_state, logprob_avg, key = sgmcmc_train_epoch(\n",
    "        params, fake_net_state, opt_state, fake_data, key)\n",
    "    if iteration % save_freq == 0:\n",
    "        all_samples.append(onp.asarray(params).copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_samples_cat = onp.stack(all_samples)\n",
    "plt.scatter(all_samples_cat[:, 0], all_samples_cat[:, 1], alpha=0.3)\n",
    "plt.grid()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SGLD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 1.e-2\n",
    "mom = 0.\n",
    "lr_schedule = train_utils.make_cosine_lr_schedule_with_burnin(lr, lr, 1)\n",
    "optimizer = sgmcmc.sgld_gradient_update(lr_schedule, momentum_decay=mom, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = jnp.ones_like(mu)\n",
    "opt_state = optimizer.init(params)\n",
    "fake_net_state = jnp.array([jnp.nan,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgmcmc_train_epoch = train_utils.make_sgd_train_epoch(\n",
    "    fake_net_apply, log_likelihood_fn, log_prior_fn, optimizer, num_batches=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:10<00:00, 963.67it/s]\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 10000\n",
    "num_devices = 1\n",
    "all_samples = []\n",
    "key = jax.random.PRNGKey(0)\n",
    "key = jax.random.split(key, num_devices)\n",
    "save_freq = 10\n",
    "\n",
    "for iteration in tqdm.tqdm(range(num_iterations)):\n",
    "    params, _, opt_state, logprob_avg, key = sgmcmc_train_epoch(\n",
    "        params, fake_net_state, opt_state, fake_data, key)\n",
    "    if iteration % save_freq == 0:\n",
    "        all_samples.append(onp.asarray(params).copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_samples_cat = onp.stack(all_samples)\n",
    "plt.scatter(all_samples_cat[:, 0], all_samples_cat[:, 1], alpha=0.3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SGHMC with RMSprop Preconditioner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 1.e-2\n",
    "mom = 0.95\n",
    "lr_schedule = train_utils.make_cosine_lr_schedule_with_burnin(lr, lr, 1)\n",
    "preconditioner = sgmcmc.get_rmsprop_preconditioner()\n",
    "optimizer = sgmcmc.sgld_gradient_update(lr_schedule, momentum_decay=mom, seed=0, preconditioner=preconditioner)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = jnp.ones_like(mu)\n",
    "opt_state = optimizer.init(params)\n",
    "fake_net_state = jnp.array([jnp.nan,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgmcmc_train_epoch = train_utils.make_sgd_train_epoch(\n",
    "    fake_net_apply, log_likelihood_fn, log_prior_fn, optimizer, num_batches=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:01<00:00, 752.14it/s]\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 1000#0\n",
    "num_devices = 1\n",
    "all_samples = []\n",
    "key = jax.random.PRNGKey(0)\n",
    "key = jax.random.split(key, num_devices)\n",
    "save_freq = 10\n",
    "\n",
    "for iteration in tqdm.tqdm(range(num_iterations)):\n",
    "    params, _, opt_state, logprob_avg, key = sgmcmc_train_epoch(\n",
    "        params, fake_net_state, opt_state, fake_data, key)\n",
    "#     print(opt_state.preconditioner_state.grad_moment_estimates)\n",
    "    if iteration % save_freq == 0:\n",
    "        all_samples.append(onp.asarray(params).copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([1.1727230e+04, 1.0309858e+00], dtype=float32)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_state.preconditioner_state.grad_moment_estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_samples_cat = onp.stack(all_samples)\n",
    "plt.scatter(all_samples_cat[:, 0], all_samples_cat[:, 1], alpha=0.3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py38",
   "language": "python",
   "name": "py38"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
